Elements of Gas Turbine Propulsion JackD.Mattingly Foreword by ' Hans von Ohain German Inventor ofthe Jet Engine GE-1014.001 GE-1014.002 ELEMENTS OF GAS TURBINE PROPULSION GE-1014.003 McGraw-Hill Series in Aer9nautical and Aerospace Engineering Consulting Editor John D. Anderson, ir., University of Maryland Anderson: Computational Fluid Dynamics: The Basics with Applications Anderson: Fundamentals of Aerodynamics Anderson: Hypersonic and High Temperature Gas Dynamics Anderson: Introduction to Flight Anderson: Modern Compressible Flow: With Historical Perspective Burton: Introduction to Dynamic Systems Analysis D'Azzo and Houpis: Linear Control System Analysis and Design Donaldson: Analysis of Aircraft Structures: An Introduction Gibson.: Principles of Composit~ Material Mechanics Kane, Likins, and Levinson: Spacecraft Dynamics Katz and Plc.itkin: Low-Speed Aerodynamics: From Wing Theory to Panel Methods Mattingly: Elements of. Gas Turbine Propulsion ~elson: Flight Stability and Automatic Control Peery and Azar: Aircraft Structures Rivello:. Theory and Analysis of Flight Structures Schlichting: Boundary Layer Theory White: Viscous Fluid Flow Wiesel: Spaceflight Dynamics GE-1014.004 McGraw-Hill Series in Mechanical Engineering Consulting Editors Jack P. Holman, Southern Methodist University John R. Lloyd, Michigan State University Anderson: Computational Fluid Kelly: Fundamentals of Mechanical Dynamics: The Basics with Applications Vibrations Anderson: Modern Compressible Flow: Kimbrell: Kinematics Analysis and With Historical Perspective Synthesis Arora: Introduction to Optimum Design Kreider and Rabi: Heating and Cooling of Bray and Stanley: Nondestructive Buildings Evaluation: A Tool for Design, Martin: Kinematics and Dynamics of Manufacturing, and Service Machines Burton: Introduction to Dynamic Systems Mattingly: Elements oj Gas Turbine Analysis Propulsion Culp: Principles of Energy Conversion Modest: Radiative Heat Transfer Dally: Packaging of Electronic Systems: A Norton: Design of Machinery Mechanical Engineering Approach Phelan: Fundamentals of Mechanical Dieter: Engineering Design: A Materials Design and Processing Approach Raven: Automatic Control Engineering Doebelin: Engineering Experimentation: Reddy: An Introduction to the Finite Planning, Execution, Reporting Element Method Driels: Linear Control Systems Rosenberg and Karnopp: Introduction to Engineering Physical Systems Dynamics Eckert and Drake: Analysis of Heat and Schlichting: Boundary-Layer Theory Mass Transfer Shames: Mechanics of Fluids Edwards and McKee: Fundamentals of Sherman: Viscous Flow Mechanical Component Design Shigley: Kinematic Analysis of Gebhart: Heat Conduction and Mass Mechanisms Diffusion Shigley and Mischke: Mechanical Gibson: Principles of Composite Material Engineering Design Mechanics Shigley and Vicker: Theory of Machines Hamrock: Fundamentals of Fluid Film and Mechanisms Lubrication Stiffler: Design with Microprocessors for Heywood: Internal Combustion Engine Mechanical Engineers Fundamentals Stoecker and Jones: Refrigeration and Air Hinze: Turbulence Conditioning Holman: Experimental Methods for Tums:.An Introduction to Combustion: Engineers Concepts and Applications Howell and Buckius: Fundamentals of Ullman:· The Mechanical Design Process Engineering Thermodynamics Vanderplaats: Numerical Optimization: Hutton: Applied Mechanical Vibrations Techniques for Engineering Design, Juvinall: Engineering Considerations of with Applications Stress, Strain, and Strength Wark: Advanced Thermodynamics for Kane and Levinson: Dynamics: Theory Engineers and Applications White: Viscous Fluid Flow . Kays and Crawford: Convective Heat and Zeid: CAD I CAM Theory and Practice Mass Transfer j GE-1014.005 ELEMENTS OF GAS TURBINE PROPULSION Jack D. Mattingly Department of Mechanical and Manufacturing Engineering Seattle University With a Foreword By Hans von Ohain McGraw-Hill, Inc. New York St. Louis San Francisco Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto GE-1014.006 _'<ELEMENTS. OF;GAS;:TURBINE PROPULSION ' ·.. ~ ~~::~ A.·~r; ... -~ ~ ·~·:~· ::· \.~~~-· ~~~·:~~·~~ :.; ~:~- ~, ·:· '.· :~. · .. · . .· ·. ·· ·· · ·- )<Copyright @)996 by McGraw-Hill, Inc. All rights reserved. Printed _in the United States 'of{\merica.·Excepi as permitted under the United States Copyright Act of1976, ho part -. ' : : . of this publication :may l:Je 'i-epi-oduced or distributed in any form or by any mearis, or ... 1i~J'.'e~( in a 'd~ta ba~e cir' retrieval system;' without the prio,r ~ritten permission of the : , -~u~~ii~e-r;:·_ - :·.: · · · · · · · · · · · }_ · · ·- 1 '.~ T~i:'-~90~ _is prift~d-o~r ~~-id-free paper. <t/ I} J - •.. -' l f13'3 1,? 3 4.~~}J::S--9:. Q DO_~ DOC 9 0 9 8 7 ~ 5 t/t: r b · · _PIN 04161~:4 ; -· :. ~' -' \ - PART'OF ,:- ';. -· -· ·: dsm.f oi(fri°912196-9 :-: ~ ->-!;;. 'f ~ '{~'-! ~-.. \-; :-~·:_-~~~.,~.. ~-~:~::·:t~} ,_ ·: :1 '.;~~-;~~; ,/ )- . ,_-:,. ;,, .·,., .~:.::.·~·-·'. ,-;-:; - ' . l,lbrary of_ Congress Ca~a-ogill,.-in-Publication Data . · . _ --~~t~~gl~:.jar;k-~;-":3-j3L?//~ 3/~7() ~6~~ , · :: :.-'./ -}:l~I_TI:e~ts ~~f ~-~s ~-u ine1prop11Ision__f.Jac_k D,•-:¥.~ttiil~ly; with a foreword by ~fans. ··~ /~-~~~~-~~~?~~--~~< (~{~~~~-~j~esin R1~~~~~;~~1: ~~gi~e~ring) . : (¥"cGra~-H1ll ~er~es m aeronautical .and !lerospace engm~ermg) :~~:~J.1i~~~~~8~~tl~Jjfj]f ~~~tf~:t·r(rf e.~.~ri~--:~~~~:-. .'._._: '.-_\-:.,, .·' -.. •'~<.~-L'Airpla11es::.'..!J.et'prcipu_lsion; · L __Title: ·: · IL;Sedes.. - . d~IIr-;' Serles:·,McGawofiilFseries- in aeroria'iitica!c°iind -ileros'pace engineering. :<!~:r;:f ~~~~~~t~;~~~,~-i·;'.;·i·.,\._.~:~;it:?' L ·: '. ~:~x,;;;J_ -.~:~_;i£(' ·• · '·- ·._·_ -·- · GE-1014.007 CONTENTS Foreword xv Preface Iv List of Symbols !ix 1 Introduction 1-1 Propulsion 1 1-2 Units and Dimensions 2 1-3 Operational Envelopes and Standard Atmosphere 4 1-4 Air-Breathing Engines 6 1-5 Aircraft Performance 33 1-6 Rocket Engines 53 Problems 60 2 Thermodynamics Review 67 2-1 Introduction 67 2-2 Definitions 68 2-3 Simple Compressible System 73 2-4 Equations of State 74 2-5 Basic Laws for a Control Mass System 76 2-6 Relations between the System and Control Volume 78 2-7 Conservation of Mass Equation 81 2-8 Steady Flow Energy Equation 81 2-9 Steady Flow Entropy Equation. 89 2-10 Momentum Equation 90 2-11 Summary of Laws for Fluid Flow 95 2-12 Perfect Gas 96 Problems 108 xi GE-1014.008 ·~ I xii CONTENTS Ii 3 Compressible Flow 114 I 3-1 Introduction 114 I 3-2 Compressible Flow Properties 114 l i 3-3 Normal Shock Wave 138 ! 3-4 Oblique Shock Wave 145 I 3-5 Steady One-Dimensional Gas Dynamics 156 I 3-6 Simple Flows 159 i I 3-7 Simple Area Flow-Nozzle Flow 161 I ! 3-8 Simple Heating Flow-Rayleigh Line 174 3-9 Simple Frictional Flow-Fanno Line 189 3-10 Summary of Simple Flows 203 Problems 206 4 Aircraft Gas Turbine Engine 213 4-1 Introduction 213 4-2 Thrust Equation 213 4-3 Note on Propulsive Efficiency 223 4-4 Gas Turbine Engine Components 224 4-5 Brayton Cycle 233 4-6 Aircraft Engine Design 236 Problems 237 5 Parametric Cycle Analysis of Ideal Engines 240 5-1 Introduction 240 5-2 Notation 241 5-3 Design Inputs 243 5-4 Steps of Engine Parametric Cycle Analysis 244 5-5 Assumptions of Ideal Cycle Analysis 246 5-6 Ideal Ramjet 246 5-7 Ideal Turbojet 256 5-8 Ideal Turbojet with Afterburner 266 5-9 Ideal Turbofan 275 5-10 Ideal Turbofan with Optimum Bypass Ratio 299 5-11 Ideal Turbofan with Optimum Fan Pressure Ratio 305 5-12 Ideal Mixed-Flow Turbofan with Afterburning 313 5-13 Ideal Turboprop Engine 322 5-14 Ideal Turboshaft Engine with Regeneration 332 Problems 337 6 Component Performance 346 6-1 Introduction 346 6-2 Variation in Gas Properties 346 6-3 Component Performance 349 6-4 Inlet and Diffuser Pressure Recovery 349 6-5 Compressor and Turbine Efficiencies 351 6-6 Burner Efficiency and Pressure Loss 360 ! i i GE-1014.009 CONTENTS xiii 6-7 Exit Nozzle Loss 361 6-8 Summary of Component Figures of Merit (Constant cP Values) 361 6-9 Component Performance with Variable cP 363 Problems 369 7 Parametric Cycle Analysis of Real Engines 371 7-1 Introduction 371 7-2 Turbojet 371 7-3 Turbojet with Afterburner 387 7-4 Turbofan-Separate Exhaust Streams 392 7-5 Turbofan with Afterburning-Separate Exhaust Streams 411 7-6 Turbofan with Afterburning-Mixed Exhaust Stream 417 7-7 Turboprop Engine 433 7-8 Variable Gas Properties 444 Problems 453 8 Engine Performance Analysis 461 8-1 Introduction 461 8-2 Gas Generator 471 8-3 Turbojet Engine 487 8-4 Turbojet with Afterburning 507 8-5 Turbofan Engine-Separate Exhausts and Convergent Nozzles 518 8-6 Turbofan with Afterburning-Mixed-Flow Exhaust Stream 541 8-7 Turboprop Engine 560 8-8 Variable Gas Properties 573 Problems 605 9 Turbo machinery 615 9-1 Introduction 615 9-2 Euler's Turbomachinery Equations 616 9-3 Axial-Flow Compressor Analysis 618 9-4 Centrifugal-Flow Compressor Analysis 676 9-5 Axial-Flow Turbine Analysis 683 9-6 Centrifugal-Flow Turbine Analysis 742 Problems 748 10 Inlets, Nozzles, and Combustion Systems 757 10-1 Introduction to Inlets and Nozzles 757 10-2 Inlets 758 10-3 Subsonic Inlets 758 10-4 Supersonic Inlets 767 10-5 Exhaust Nozzles 796 10-6 Introduction to Combustion Systems 814 10-7 Main Burners 827 10-8 Afterburners 838 Problems 849 GE-1014.010 xiv coNTENTs I Appendixes 853 A U.S. Standard Atmosphere, 1976 855 B Gas Turbine Engine Data 860 C Data for Some Liquid Propellant Rocket Engines 865 D Air and (CH2 )n Properties at Low Pressure 867 E Compressible Flow Functions ( y = 1.4, 1.33, and 1.3) 878 F Normal Shock Functions ( y = 1.4) 897 G Two-Dimensional Oblique Shock Functions ( y = 1.4) 902 H Rayleigh Line Flow Functions ( y ~ 1.4) 910 I Fanno Line Flow Functions ( y = 1.4) 917 J Turbomachinery Stresses and Materials 924 K About the Software 938 References 945 Index 949 I ! I _j GE-1014.011 Ix LIST OF SYMBOLS f fuel/air ratio; function FR thrust ratio [Eq. (5-56)] g acceleration of gravity gc Newton's constant go acceleration of gravity at sea level H enthalpy h enthalpy per unit mass; height hPR low heating value of fuel 2 I impulse function [ = PA(l + yM )] Isp specific impulse [Eq.